Larger perimeter

There are a square and a circle that passes through two adjacent vertices of the square (end points of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter?

Correct result:

x =  1

Solution:

a=1  r2=(a/2)2+(ar)2 r2=a2/4+a22ar+r2 2ar=a2/4+a2 2r=a/4+a r=a/8+a/2 r=58 a=58 1=58=0.625   o1=4 a=4 1=4 o2=2π r=2 3.1416 0.6253.927  o1>o2 x=1



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